Polytope of Type {20,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,24}*1920a
if this polytope has a name.
Group : SmallGroup(1920,13408)
Rank : 3
Schlafli Type : {20,24}
Number of vertices, edges, etc : 40, 480, 48
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {20,12}*960a, {20,24}*960a, {20,24}*960b
3-fold quotients : {20,8}*640a
4-fold quotients : {10,24}*480, {20,12}*480
5-fold quotients : {4,24}*384a
6-fold quotients : {20,4}*320, {20,8}*320a, {20,8}*320b
8-fold quotients : {10,12}*240, {20,6}*240a
10-fold quotients : {4,24}*192a, {4,12}*192a, {4,24}*192b
12-fold quotients : {20,4}*160, {10,8}*160
15-fold quotients : {4,8}*128a
16-fold quotients : {10,6}*120
20-fold quotients : {4,12}*96a, {2,24}*96
24-fold quotients : {20,2}*80, {10,4}*80
30-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
40-fold quotients : {2,12}*48, {4,6}*48a
48-fold quotients : {10,2}*40
60-fold quotients : {4,4}*32, {2,8}*32
80-fold quotients : {2,6}*24
96-fold quotients : {5,2}*20
120-fold quotients : {2,4}*16, {4,2}*16
160-fold quotients : {2,3}*12
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,241)( 2,245)( 3,244)( 4,243)( 5,242)( 6,246)( 7,250)( 8,249)
( 9,248)( 10,247)( 11,251)( 12,255)( 13,254)( 14,253)( 15,252)( 16,256)
( 17,260)( 18,259)( 19,258)( 20,257)( 21,261)( 22,265)( 23,264)( 24,263)
( 25,262)( 26,266)( 27,270)( 28,269)( 29,268)( 30,267)( 31,271)( 32,275)
( 33,274)( 34,273)( 35,272)( 36,276)( 37,280)( 38,279)( 39,278)( 40,277)
( 41,281)( 42,285)( 43,284)( 44,283)( 45,282)( 46,286)( 47,290)( 48,289)
( 49,288)( 50,287)( 51,291)( 52,295)( 53,294)( 54,293)( 55,292)( 56,296)
( 57,300)( 58,299)( 59,298)( 60,297)( 61,301)( 62,305)( 63,304)( 64,303)
( 65,302)( 66,306)( 67,310)( 68,309)( 69,308)( 70,307)( 71,311)( 72,315)
( 73,314)( 74,313)( 75,312)( 76,316)( 77,320)( 78,319)( 79,318)( 80,317)
( 81,321)( 82,325)( 83,324)( 84,323)( 85,322)( 86,326)( 87,330)( 88,329)
( 89,328)( 90,327)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)( 96,336)
( 97,340)( 98,339)( 99,338)(100,337)(101,341)(102,345)(103,344)(104,343)
(105,342)(106,346)(107,350)(108,349)(109,348)(110,347)(111,351)(112,355)
(113,354)(114,353)(115,352)(116,356)(117,360)(118,359)(119,358)(120,357)
(121,376)(122,380)(123,379)(124,378)(125,377)(126,381)(127,385)(128,384)
(129,383)(130,382)(131,386)(132,390)(133,389)(134,388)(135,387)(136,361)
(137,365)(138,364)(139,363)(140,362)(141,366)(142,370)(143,369)(144,368)
(145,367)(146,371)(147,375)(148,374)(149,373)(150,372)(151,406)(152,410)
(153,409)(154,408)(155,407)(156,411)(157,415)(158,414)(159,413)(160,412)
(161,416)(162,420)(163,419)(164,418)(165,417)(166,391)(167,395)(168,394)
(169,393)(170,392)(171,396)(172,400)(173,399)(174,398)(175,397)(176,401)
(177,405)(178,404)(179,403)(180,402)(181,436)(182,440)(183,439)(184,438)
(185,437)(186,441)(187,445)(188,444)(189,443)(190,442)(191,446)(192,450)
(193,449)(194,448)(195,447)(196,421)(197,425)(198,424)(199,423)(200,422)
(201,426)(202,430)(203,429)(204,428)(205,427)(206,431)(207,435)(208,434)
(209,433)(210,432)(211,466)(212,470)(213,469)(214,468)(215,467)(216,471)
(217,475)(218,474)(219,473)(220,472)(221,476)(222,480)(223,479)(224,478)
(225,477)(226,451)(227,455)(228,454)(229,453)(230,452)(231,456)(232,460)
(233,459)(234,458)(235,457)(236,461)(237,465)(238,464)(239,463)(240,462)
(481,721)(482,725)(483,724)(484,723)(485,722)(486,726)(487,730)(488,729)
(489,728)(490,727)(491,731)(492,735)(493,734)(494,733)(495,732)(496,736)
(497,740)(498,739)(499,738)(500,737)(501,741)(502,745)(503,744)(504,743)
(505,742)(506,746)(507,750)(508,749)(509,748)(510,747)(511,751)(512,755)
(513,754)(514,753)(515,752)(516,756)(517,760)(518,759)(519,758)(520,757)
(521,761)(522,765)(523,764)(524,763)(525,762)(526,766)(527,770)(528,769)
(529,768)(530,767)(531,771)(532,775)(533,774)(534,773)(535,772)(536,776)
(537,780)(538,779)(539,778)(540,777)(541,781)(542,785)(543,784)(544,783)
(545,782)(546,786)(547,790)(548,789)(549,788)(550,787)(551,791)(552,795)
(553,794)(554,793)(555,792)(556,796)(557,800)(558,799)(559,798)(560,797)
(561,801)(562,805)(563,804)(564,803)(565,802)(566,806)(567,810)(568,809)
(569,808)(570,807)(571,811)(572,815)(573,814)(574,813)(575,812)(576,816)
(577,820)(578,819)(579,818)(580,817)(581,821)(582,825)(583,824)(584,823)
(585,822)(586,826)(587,830)(588,829)(589,828)(590,827)(591,831)(592,835)
(593,834)(594,833)(595,832)(596,836)(597,840)(598,839)(599,838)(600,837)
(601,856)(602,860)(603,859)(604,858)(605,857)(606,861)(607,865)(608,864)
(609,863)(610,862)(611,866)(612,870)(613,869)(614,868)(615,867)(616,841)
(617,845)(618,844)(619,843)(620,842)(621,846)(622,850)(623,849)(624,848)
(625,847)(626,851)(627,855)(628,854)(629,853)(630,852)(631,886)(632,890)
(633,889)(634,888)(635,887)(636,891)(637,895)(638,894)(639,893)(640,892)
(641,896)(642,900)(643,899)(644,898)(645,897)(646,871)(647,875)(648,874)
(649,873)(650,872)(651,876)(652,880)(653,879)(654,878)(655,877)(656,881)
(657,885)(658,884)(659,883)(660,882)(661,916)(662,920)(663,919)(664,918)
(665,917)(666,921)(667,925)(668,924)(669,923)(670,922)(671,926)(672,930)
(673,929)(674,928)(675,927)(676,901)(677,905)(678,904)(679,903)(680,902)
(681,906)(682,910)(683,909)(684,908)(685,907)(686,911)(687,915)(688,914)
(689,913)(690,912)(691,946)(692,950)(693,949)(694,948)(695,947)(696,951)
(697,955)(698,954)(699,953)(700,952)(701,956)(702,960)(703,959)(704,958)
(705,957)(706,931)(707,935)(708,934)(709,933)(710,932)(711,936)(712,940)
(713,939)(714,938)(715,937)(716,941)(717,945)(718,944)(719,943)(720,942);;
s1 := ( 1, 2)( 3, 5)( 6, 12)( 7, 11)( 8, 15)( 9, 14)( 10, 13)( 16, 17)
( 18, 20)( 21, 27)( 22, 26)( 23, 30)( 24, 29)( 25, 28)( 31, 32)( 33, 35)
( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)( 46, 47)( 48, 50)( 51, 57)
( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 62)( 63, 65)( 66, 72)( 67, 71)
( 68, 75)( 69, 74)( 70, 73)( 76, 77)( 78, 80)( 81, 87)( 82, 86)( 83, 90)
( 84, 89)( 85, 88)( 91, 92)( 93, 95)( 96,102)( 97,101)( 98,105)( 99,104)
(100,103)(106,107)(108,110)(111,117)(112,116)(113,120)(114,119)(115,118)
(121,152)(122,151)(123,155)(124,154)(125,153)(126,162)(127,161)(128,165)
(129,164)(130,163)(131,157)(132,156)(133,160)(134,159)(135,158)(136,167)
(137,166)(138,170)(139,169)(140,168)(141,177)(142,176)(143,180)(144,179)
(145,178)(146,172)(147,171)(148,175)(149,174)(150,173)(181,212)(182,211)
(183,215)(184,214)(185,213)(186,222)(187,221)(188,225)(189,224)(190,223)
(191,217)(192,216)(193,220)(194,219)(195,218)(196,227)(197,226)(198,230)
(199,229)(200,228)(201,237)(202,236)(203,240)(204,239)(205,238)(206,232)
(207,231)(208,235)(209,234)(210,233)(241,302)(242,301)(243,305)(244,304)
(245,303)(246,312)(247,311)(248,315)(249,314)(250,313)(251,307)(252,306)
(253,310)(254,309)(255,308)(256,317)(257,316)(258,320)(259,319)(260,318)
(261,327)(262,326)(263,330)(264,329)(265,328)(266,322)(267,321)(268,325)
(269,324)(270,323)(271,332)(272,331)(273,335)(274,334)(275,333)(276,342)
(277,341)(278,345)(279,344)(280,343)(281,337)(282,336)(283,340)(284,339)
(285,338)(286,347)(287,346)(288,350)(289,349)(290,348)(291,357)(292,356)
(293,360)(294,359)(295,358)(296,352)(297,351)(298,355)(299,354)(300,353)
(361,452)(362,451)(363,455)(364,454)(365,453)(366,462)(367,461)(368,465)
(369,464)(370,463)(371,457)(372,456)(373,460)(374,459)(375,458)(376,467)
(377,466)(378,470)(379,469)(380,468)(381,477)(382,476)(383,480)(384,479)
(385,478)(386,472)(387,471)(388,475)(389,474)(390,473)(391,422)(392,421)
(393,425)(394,424)(395,423)(396,432)(397,431)(398,435)(399,434)(400,433)
(401,427)(402,426)(403,430)(404,429)(405,428)(406,437)(407,436)(408,440)
(409,439)(410,438)(411,447)(412,446)(413,450)(414,449)(415,448)(416,442)
(417,441)(418,445)(419,444)(420,443)(481,602)(482,601)(483,605)(484,604)
(485,603)(486,612)(487,611)(488,615)(489,614)(490,613)(491,607)(492,606)
(493,610)(494,609)(495,608)(496,617)(497,616)(498,620)(499,619)(500,618)
(501,627)(502,626)(503,630)(504,629)(505,628)(506,622)(507,621)(508,625)
(509,624)(510,623)(511,632)(512,631)(513,635)(514,634)(515,633)(516,642)
(517,641)(518,645)(519,644)(520,643)(521,637)(522,636)(523,640)(524,639)
(525,638)(526,647)(527,646)(528,650)(529,649)(530,648)(531,657)(532,656)
(533,660)(534,659)(535,658)(536,652)(537,651)(538,655)(539,654)(540,653)
(541,662)(542,661)(543,665)(544,664)(545,663)(546,672)(547,671)(548,675)
(549,674)(550,673)(551,667)(552,666)(553,670)(554,669)(555,668)(556,677)
(557,676)(558,680)(559,679)(560,678)(561,687)(562,686)(563,690)(564,689)
(565,688)(566,682)(567,681)(568,685)(569,684)(570,683)(571,692)(572,691)
(573,695)(574,694)(575,693)(576,702)(577,701)(578,705)(579,704)(580,703)
(581,697)(582,696)(583,700)(584,699)(585,698)(586,707)(587,706)(588,710)
(589,709)(590,708)(591,717)(592,716)(593,720)(594,719)(595,718)(596,712)
(597,711)(598,715)(599,714)(600,713)(721,917)(722,916)(723,920)(724,919)
(725,918)(726,927)(727,926)(728,930)(729,929)(730,928)(731,922)(732,921)
(733,925)(734,924)(735,923)(736,902)(737,901)(738,905)(739,904)(740,903)
(741,912)(742,911)(743,915)(744,914)(745,913)(746,907)(747,906)(748,910)
(749,909)(750,908)(751,947)(752,946)(753,950)(754,949)(755,948)(756,957)
(757,956)(758,960)(759,959)(760,958)(761,952)(762,951)(763,955)(764,954)
(765,953)(766,932)(767,931)(768,935)(769,934)(770,933)(771,942)(772,941)
(773,945)(774,944)(775,943)(776,937)(777,936)(778,940)(779,939)(780,938)
(781,857)(782,856)(783,860)(784,859)(785,858)(786,867)(787,866)(788,870)
(789,869)(790,868)(791,862)(792,861)(793,865)(794,864)(795,863)(796,842)
(797,841)(798,845)(799,844)(800,843)(801,852)(802,851)(803,855)(804,854)
(805,853)(806,847)(807,846)(808,850)(809,849)(810,848)(811,887)(812,886)
(813,890)(814,889)(815,888)(816,897)(817,896)(818,900)(819,899)(820,898)
(821,892)(822,891)(823,895)(824,894)(825,893)(826,872)(827,871)(828,875)
(829,874)(830,873)(831,882)(832,881)(833,885)(834,884)(835,883)(836,877)
(837,876)(838,880)(839,879)(840,878);;
s2 := ( 1,726)( 2,727)( 3,728)( 4,729)( 5,730)( 6,721)( 7,722)( 8,723)
( 9,724)( 10,725)( 11,731)( 12,732)( 13,733)( 14,734)( 15,735)( 16,741)
( 17,742)( 18,743)( 19,744)( 20,745)( 21,736)( 22,737)( 23,738)( 24,739)
( 25,740)( 26,746)( 27,747)( 28,748)( 29,749)( 30,750)( 31,756)( 32,757)
( 33,758)( 34,759)( 35,760)( 36,751)( 37,752)( 38,753)( 39,754)( 40,755)
( 41,761)( 42,762)( 43,763)( 44,764)( 45,765)( 46,771)( 47,772)( 48,773)
( 49,774)( 50,775)( 51,766)( 52,767)( 53,768)( 54,769)( 55,770)( 56,776)
( 57,777)( 58,778)( 59,779)( 60,780)( 61,801)( 62,802)( 63,803)( 64,804)
( 65,805)( 66,796)( 67,797)( 68,798)( 69,799)( 70,800)( 71,806)( 72,807)
( 73,808)( 74,809)( 75,810)( 76,786)( 77,787)( 78,788)( 79,789)( 80,790)
( 81,781)( 82,782)( 83,783)( 84,784)( 85,785)( 86,791)( 87,792)( 88,793)
( 89,794)( 90,795)( 91,831)( 92,832)( 93,833)( 94,834)( 95,835)( 96,826)
( 97,827)( 98,828)( 99,829)(100,830)(101,836)(102,837)(103,838)(104,839)
(105,840)(106,816)(107,817)(108,818)(109,819)(110,820)(111,811)(112,812)
(113,813)(114,814)(115,815)(116,821)(117,822)(118,823)(119,824)(120,825)
(121,891)(122,892)(123,893)(124,894)(125,895)(126,886)(127,887)(128,888)
(129,889)(130,890)(131,896)(132,897)(133,898)(134,899)(135,900)(136,876)
(137,877)(138,878)(139,879)(140,880)(141,871)(142,872)(143,873)(144,874)
(145,875)(146,881)(147,882)(148,883)(149,884)(150,885)(151,861)(152,862)
(153,863)(154,864)(155,865)(156,856)(157,857)(158,858)(159,859)(160,860)
(161,866)(162,867)(163,868)(164,869)(165,870)(166,846)(167,847)(168,848)
(169,849)(170,850)(171,841)(172,842)(173,843)(174,844)(175,845)(176,851)
(177,852)(178,853)(179,854)(180,855)(181,936)(182,937)(183,938)(184,939)
(185,940)(186,931)(187,932)(188,933)(189,934)(190,935)(191,941)(192,942)
(193,943)(194,944)(195,945)(196,951)(197,952)(198,953)(199,954)(200,955)
(201,946)(202,947)(203,948)(204,949)(205,950)(206,956)(207,957)(208,958)
(209,959)(210,960)(211,906)(212,907)(213,908)(214,909)(215,910)(216,901)
(217,902)(218,903)(219,904)(220,905)(221,911)(222,912)(223,913)(224,914)
(225,915)(226,921)(227,922)(228,923)(229,924)(230,925)(231,916)(232,917)
(233,918)(234,919)(235,920)(236,926)(237,927)(238,928)(239,929)(240,930)
(241,486)(242,487)(243,488)(244,489)(245,490)(246,481)(247,482)(248,483)
(249,484)(250,485)(251,491)(252,492)(253,493)(254,494)(255,495)(256,501)
(257,502)(258,503)(259,504)(260,505)(261,496)(262,497)(263,498)(264,499)
(265,500)(266,506)(267,507)(268,508)(269,509)(270,510)(271,516)(272,517)
(273,518)(274,519)(275,520)(276,511)(277,512)(278,513)(279,514)(280,515)
(281,521)(282,522)(283,523)(284,524)(285,525)(286,531)(287,532)(288,533)
(289,534)(290,535)(291,526)(292,527)(293,528)(294,529)(295,530)(296,536)
(297,537)(298,538)(299,539)(300,540)(301,561)(302,562)(303,563)(304,564)
(305,565)(306,556)(307,557)(308,558)(309,559)(310,560)(311,566)(312,567)
(313,568)(314,569)(315,570)(316,546)(317,547)(318,548)(319,549)(320,550)
(321,541)(322,542)(323,543)(324,544)(325,545)(326,551)(327,552)(328,553)
(329,554)(330,555)(331,591)(332,592)(333,593)(334,594)(335,595)(336,586)
(337,587)(338,588)(339,589)(340,590)(341,596)(342,597)(343,598)(344,599)
(345,600)(346,576)(347,577)(348,578)(349,579)(350,580)(351,571)(352,572)
(353,573)(354,574)(355,575)(356,581)(357,582)(358,583)(359,584)(360,585)
(361,651)(362,652)(363,653)(364,654)(365,655)(366,646)(367,647)(368,648)
(369,649)(370,650)(371,656)(372,657)(373,658)(374,659)(375,660)(376,636)
(377,637)(378,638)(379,639)(380,640)(381,631)(382,632)(383,633)(384,634)
(385,635)(386,641)(387,642)(388,643)(389,644)(390,645)(391,621)(392,622)
(393,623)(394,624)(395,625)(396,616)(397,617)(398,618)(399,619)(400,620)
(401,626)(402,627)(403,628)(404,629)(405,630)(406,606)(407,607)(408,608)
(409,609)(410,610)(411,601)(412,602)(413,603)(414,604)(415,605)(416,611)
(417,612)(418,613)(419,614)(420,615)(421,696)(422,697)(423,698)(424,699)
(425,700)(426,691)(427,692)(428,693)(429,694)(430,695)(431,701)(432,702)
(433,703)(434,704)(435,705)(436,711)(437,712)(438,713)(439,714)(440,715)
(441,706)(442,707)(443,708)(444,709)(445,710)(446,716)(447,717)(448,718)
(449,719)(450,720)(451,666)(452,667)(453,668)(454,669)(455,670)(456,661)
(457,662)(458,663)(459,664)(460,665)(461,671)(462,672)(463,673)(464,674)
(465,675)(466,681)(467,682)(468,683)(469,684)(470,685)(471,676)(472,677)
(473,678)(474,679)(475,680)(476,686)(477,687)(478,688)(479,689)(480,690);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,241)( 2,245)( 3,244)( 4,243)( 5,242)( 6,246)( 7,250)
( 8,249)( 9,248)( 10,247)( 11,251)( 12,255)( 13,254)( 14,253)( 15,252)
( 16,256)( 17,260)( 18,259)( 19,258)( 20,257)( 21,261)( 22,265)( 23,264)
( 24,263)( 25,262)( 26,266)( 27,270)( 28,269)( 29,268)( 30,267)( 31,271)
( 32,275)( 33,274)( 34,273)( 35,272)( 36,276)( 37,280)( 38,279)( 39,278)
( 40,277)( 41,281)( 42,285)( 43,284)( 44,283)( 45,282)( 46,286)( 47,290)
( 48,289)( 49,288)( 50,287)( 51,291)( 52,295)( 53,294)( 54,293)( 55,292)
( 56,296)( 57,300)( 58,299)( 59,298)( 60,297)( 61,301)( 62,305)( 63,304)
( 64,303)( 65,302)( 66,306)( 67,310)( 68,309)( 69,308)( 70,307)( 71,311)
( 72,315)( 73,314)( 74,313)( 75,312)( 76,316)( 77,320)( 78,319)( 79,318)
( 80,317)( 81,321)( 82,325)( 83,324)( 84,323)( 85,322)( 86,326)( 87,330)
( 88,329)( 89,328)( 90,327)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)
( 96,336)( 97,340)( 98,339)( 99,338)(100,337)(101,341)(102,345)(103,344)
(104,343)(105,342)(106,346)(107,350)(108,349)(109,348)(110,347)(111,351)
(112,355)(113,354)(114,353)(115,352)(116,356)(117,360)(118,359)(119,358)
(120,357)(121,376)(122,380)(123,379)(124,378)(125,377)(126,381)(127,385)
(128,384)(129,383)(130,382)(131,386)(132,390)(133,389)(134,388)(135,387)
(136,361)(137,365)(138,364)(139,363)(140,362)(141,366)(142,370)(143,369)
(144,368)(145,367)(146,371)(147,375)(148,374)(149,373)(150,372)(151,406)
(152,410)(153,409)(154,408)(155,407)(156,411)(157,415)(158,414)(159,413)
(160,412)(161,416)(162,420)(163,419)(164,418)(165,417)(166,391)(167,395)
(168,394)(169,393)(170,392)(171,396)(172,400)(173,399)(174,398)(175,397)
(176,401)(177,405)(178,404)(179,403)(180,402)(181,436)(182,440)(183,439)
(184,438)(185,437)(186,441)(187,445)(188,444)(189,443)(190,442)(191,446)
(192,450)(193,449)(194,448)(195,447)(196,421)(197,425)(198,424)(199,423)
(200,422)(201,426)(202,430)(203,429)(204,428)(205,427)(206,431)(207,435)
(208,434)(209,433)(210,432)(211,466)(212,470)(213,469)(214,468)(215,467)
(216,471)(217,475)(218,474)(219,473)(220,472)(221,476)(222,480)(223,479)
(224,478)(225,477)(226,451)(227,455)(228,454)(229,453)(230,452)(231,456)
(232,460)(233,459)(234,458)(235,457)(236,461)(237,465)(238,464)(239,463)
(240,462)(481,721)(482,725)(483,724)(484,723)(485,722)(486,726)(487,730)
(488,729)(489,728)(490,727)(491,731)(492,735)(493,734)(494,733)(495,732)
(496,736)(497,740)(498,739)(499,738)(500,737)(501,741)(502,745)(503,744)
(504,743)(505,742)(506,746)(507,750)(508,749)(509,748)(510,747)(511,751)
(512,755)(513,754)(514,753)(515,752)(516,756)(517,760)(518,759)(519,758)
(520,757)(521,761)(522,765)(523,764)(524,763)(525,762)(526,766)(527,770)
(528,769)(529,768)(530,767)(531,771)(532,775)(533,774)(534,773)(535,772)
(536,776)(537,780)(538,779)(539,778)(540,777)(541,781)(542,785)(543,784)
(544,783)(545,782)(546,786)(547,790)(548,789)(549,788)(550,787)(551,791)
(552,795)(553,794)(554,793)(555,792)(556,796)(557,800)(558,799)(559,798)
(560,797)(561,801)(562,805)(563,804)(564,803)(565,802)(566,806)(567,810)
(568,809)(569,808)(570,807)(571,811)(572,815)(573,814)(574,813)(575,812)
(576,816)(577,820)(578,819)(579,818)(580,817)(581,821)(582,825)(583,824)
(584,823)(585,822)(586,826)(587,830)(588,829)(589,828)(590,827)(591,831)
(592,835)(593,834)(594,833)(595,832)(596,836)(597,840)(598,839)(599,838)
(600,837)(601,856)(602,860)(603,859)(604,858)(605,857)(606,861)(607,865)
(608,864)(609,863)(610,862)(611,866)(612,870)(613,869)(614,868)(615,867)
(616,841)(617,845)(618,844)(619,843)(620,842)(621,846)(622,850)(623,849)
(624,848)(625,847)(626,851)(627,855)(628,854)(629,853)(630,852)(631,886)
(632,890)(633,889)(634,888)(635,887)(636,891)(637,895)(638,894)(639,893)
(640,892)(641,896)(642,900)(643,899)(644,898)(645,897)(646,871)(647,875)
(648,874)(649,873)(650,872)(651,876)(652,880)(653,879)(654,878)(655,877)
(656,881)(657,885)(658,884)(659,883)(660,882)(661,916)(662,920)(663,919)
(664,918)(665,917)(666,921)(667,925)(668,924)(669,923)(670,922)(671,926)
(672,930)(673,929)(674,928)(675,927)(676,901)(677,905)(678,904)(679,903)
(680,902)(681,906)(682,910)(683,909)(684,908)(685,907)(686,911)(687,915)
(688,914)(689,913)(690,912)(691,946)(692,950)(693,949)(694,948)(695,947)
(696,951)(697,955)(698,954)(699,953)(700,952)(701,956)(702,960)(703,959)
(704,958)(705,957)(706,931)(707,935)(708,934)(709,933)(710,932)(711,936)
(712,940)(713,939)(714,938)(715,937)(716,941)(717,945)(718,944)(719,943)
(720,942);
s1 := Sym(960)!( 1, 2)( 3, 5)( 6, 12)( 7, 11)( 8, 15)( 9, 14)( 10, 13)
( 16, 17)( 18, 20)( 21, 27)( 22, 26)( 23, 30)( 24, 29)( 25, 28)( 31, 32)
( 33, 35)( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)( 46, 47)( 48, 50)
( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 62)( 63, 65)( 66, 72)
( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 77)( 78, 80)( 81, 87)( 82, 86)
( 83, 90)( 84, 89)( 85, 88)( 91, 92)( 93, 95)( 96,102)( 97,101)( 98,105)
( 99,104)(100,103)(106,107)(108,110)(111,117)(112,116)(113,120)(114,119)
(115,118)(121,152)(122,151)(123,155)(124,154)(125,153)(126,162)(127,161)
(128,165)(129,164)(130,163)(131,157)(132,156)(133,160)(134,159)(135,158)
(136,167)(137,166)(138,170)(139,169)(140,168)(141,177)(142,176)(143,180)
(144,179)(145,178)(146,172)(147,171)(148,175)(149,174)(150,173)(181,212)
(182,211)(183,215)(184,214)(185,213)(186,222)(187,221)(188,225)(189,224)
(190,223)(191,217)(192,216)(193,220)(194,219)(195,218)(196,227)(197,226)
(198,230)(199,229)(200,228)(201,237)(202,236)(203,240)(204,239)(205,238)
(206,232)(207,231)(208,235)(209,234)(210,233)(241,302)(242,301)(243,305)
(244,304)(245,303)(246,312)(247,311)(248,315)(249,314)(250,313)(251,307)
(252,306)(253,310)(254,309)(255,308)(256,317)(257,316)(258,320)(259,319)
(260,318)(261,327)(262,326)(263,330)(264,329)(265,328)(266,322)(267,321)
(268,325)(269,324)(270,323)(271,332)(272,331)(273,335)(274,334)(275,333)
(276,342)(277,341)(278,345)(279,344)(280,343)(281,337)(282,336)(283,340)
(284,339)(285,338)(286,347)(287,346)(288,350)(289,349)(290,348)(291,357)
(292,356)(293,360)(294,359)(295,358)(296,352)(297,351)(298,355)(299,354)
(300,353)(361,452)(362,451)(363,455)(364,454)(365,453)(366,462)(367,461)
(368,465)(369,464)(370,463)(371,457)(372,456)(373,460)(374,459)(375,458)
(376,467)(377,466)(378,470)(379,469)(380,468)(381,477)(382,476)(383,480)
(384,479)(385,478)(386,472)(387,471)(388,475)(389,474)(390,473)(391,422)
(392,421)(393,425)(394,424)(395,423)(396,432)(397,431)(398,435)(399,434)
(400,433)(401,427)(402,426)(403,430)(404,429)(405,428)(406,437)(407,436)
(408,440)(409,439)(410,438)(411,447)(412,446)(413,450)(414,449)(415,448)
(416,442)(417,441)(418,445)(419,444)(420,443)(481,602)(482,601)(483,605)
(484,604)(485,603)(486,612)(487,611)(488,615)(489,614)(490,613)(491,607)
(492,606)(493,610)(494,609)(495,608)(496,617)(497,616)(498,620)(499,619)
(500,618)(501,627)(502,626)(503,630)(504,629)(505,628)(506,622)(507,621)
(508,625)(509,624)(510,623)(511,632)(512,631)(513,635)(514,634)(515,633)
(516,642)(517,641)(518,645)(519,644)(520,643)(521,637)(522,636)(523,640)
(524,639)(525,638)(526,647)(527,646)(528,650)(529,649)(530,648)(531,657)
(532,656)(533,660)(534,659)(535,658)(536,652)(537,651)(538,655)(539,654)
(540,653)(541,662)(542,661)(543,665)(544,664)(545,663)(546,672)(547,671)
(548,675)(549,674)(550,673)(551,667)(552,666)(553,670)(554,669)(555,668)
(556,677)(557,676)(558,680)(559,679)(560,678)(561,687)(562,686)(563,690)
(564,689)(565,688)(566,682)(567,681)(568,685)(569,684)(570,683)(571,692)
(572,691)(573,695)(574,694)(575,693)(576,702)(577,701)(578,705)(579,704)
(580,703)(581,697)(582,696)(583,700)(584,699)(585,698)(586,707)(587,706)
(588,710)(589,709)(590,708)(591,717)(592,716)(593,720)(594,719)(595,718)
(596,712)(597,711)(598,715)(599,714)(600,713)(721,917)(722,916)(723,920)
(724,919)(725,918)(726,927)(727,926)(728,930)(729,929)(730,928)(731,922)
(732,921)(733,925)(734,924)(735,923)(736,902)(737,901)(738,905)(739,904)
(740,903)(741,912)(742,911)(743,915)(744,914)(745,913)(746,907)(747,906)
(748,910)(749,909)(750,908)(751,947)(752,946)(753,950)(754,949)(755,948)
(756,957)(757,956)(758,960)(759,959)(760,958)(761,952)(762,951)(763,955)
(764,954)(765,953)(766,932)(767,931)(768,935)(769,934)(770,933)(771,942)
(772,941)(773,945)(774,944)(775,943)(776,937)(777,936)(778,940)(779,939)
(780,938)(781,857)(782,856)(783,860)(784,859)(785,858)(786,867)(787,866)
(788,870)(789,869)(790,868)(791,862)(792,861)(793,865)(794,864)(795,863)
(796,842)(797,841)(798,845)(799,844)(800,843)(801,852)(802,851)(803,855)
(804,854)(805,853)(806,847)(807,846)(808,850)(809,849)(810,848)(811,887)
(812,886)(813,890)(814,889)(815,888)(816,897)(817,896)(818,900)(819,899)
(820,898)(821,892)(822,891)(823,895)(824,894)(825,893)(826,872)(827,871)
(828,875)(829,874)(830,873)(831,882)(832,881)(833,885)(834,884)(835,883)
(836,877)(837,876)(838,880)(839,879)(840,878);
s2 := Sym(960)!( 1,726)( 2,727)( 3,728)( 4,729)( 5,730)( 6,721)( 7,722)
( 8,723)( 9,724)( 10,725)( 11,731)( 12,732)( 13,733)( 14,734)( 15,735)
( 16,741)( 17,742)( 18,743)( 19,744)( 20,745)( 21,736)( 22,737)( 23,738)
( 24,739)( 25,740)( 26,746)( 27,747)( 28,748)( 29,749)( 30,750)( 31,756)
( 32,757)( 33,758)( 34,759)( 35,760)( 36,751)( 37,752)( 38,753)( 39,754)
( 40,755)( 41,761)( 42,762)( 43,763)( 44,764)( 45,765)( 46,771)( 47,772)
( 48,773)( 49,774)( 50,775)( 51,766)( 52,767)( 53,768)( 54,769)( 55,770)
( 56,776)( 57,777)( 58,778)( 59,779)( 60,780)( 61,801)( 62,802)( 63,803)
( 64,804)( 65,805)( 66,796)( 67,797)( 68,798)( 69,799)( 70,800)( 71,806)
( 72,807)( 73,808)( 74,809)( 75,810)( 76,786)( 77,787)( 78,788)( 79,789)
( 80,790)( 81,781)( 82,782)( 83,783)( 84,784)( 85,785)( 86,791)( 87,792)
( 88,793)( 89,794)( 90,795)( 91,831)( 92,832)( 93,833)( 94,834)( 95,835)
( 96,826)( 97,827)( 98,828)( 99,829)(100,830)(101,836)(102,837)(103,838)
(104,839)(105,840)(106,816)(107,817)(108,818)(109,819)(110,820)(111,811)
(112,812)(113,813)(114,814)(115,815)(116,821)(117,822)(118,823)(119,824)
(120,825)(121,891)(122,892)(123,893)(124,894)(125,895)(126,886)(127,887)
(128,888)(129,889)(130,890)(131,896)(132,897)(133,898)(134,899)(135,900)
(136,876)(137,877)(138,878)(139,879)(140,880)(141,871)(142,872)(143,873)
(144,874)(145,875)(146,881)(147,882)(148,883)(149,884)(150,885)(151,861)
(152,862)(153,863)(154,864)(155,865)(156,856)(157,857)(158,858)(159,859)
(160,860)(161,866)(162,867)(163,868)(164,869)(165,870)(166,846)(167,847)
(168,848)(169,849)(170,850)(171,841)(172,842)(173,843)(174,844)(175,845)
(176,851)(177,852)(178,853)(179,854)(180,855)(181,936)(182,937)(183,938)
(184,939)(185,940)(186,931)(187,932)(188,933)(189,934)(190,935)(191,941)
(192,942)(193,943)(194,944)(195,945)(196,951)(197,952)(198,953)(199,954)
(200,955)(201,946)(202,947)(203,948)(204,949)(205,950)(206,956)(207,957)
(208,958)(209,959)(210,960)(211,906)(212,907)(213,908)(214,909)(215,910)
(216,901)(217,902)(218,903)(219,904)(220,905)(221,911)(222,912)(223,913)
(224,914)(225,915)(226,921)(227,922)(228,923)(229,924)(230,925)(231,916)
(232,917)(233,918)(234,919)(235,920)(236,926)(237,927)(238,928)(239,929)
(240,930)(241,486)(242,487)(243,488)(244,489)(245,490)(246,481)(247,482)
(248,483)(249,484)(250,485)(251,491)(252,492)(253,493)(254,494)(255,495)
(256,501)(257,502)(258,503)(259,504)(260,505)(261,496)(262,497)(263,498)
(264,499)(265,500)(266,506)(267,507)(268,508)(269,509)(270,510)(271,516)
(272,517)(273,518)(274,519)(275,520)(276,511)(277,512)(278,513)(279,514)
(280,515)(281,521)(282,522)(283,523)(284,524)(285,525)(286,531)(287,532)
(288,533)(289,534)(290,535)(291,526)(292,527)(293,528)(294,529)(295,530)
(296,536)(297,537)(298,538)(299,539)(300,540)(301,561)(302,562)(303,563)
(304,564)(305,565)(306,556)(307,557)(308,558)(309,559)(310,560)(311,566)
(312,567)(313,568)(314,569)(315,570)(316,546)(317,547)(318,548)(319,549)
(320,550)(321,541)(322,542)(323,543)(324,544)(325,545)(326,551)(327,552)
(328,553)(329,554)(330,555)(331,591)(332,592)(333,593)(334,594)(335,595)
(336,586)(337,587)(338,588)(339,589)(340,590)(341,596)(342,597)(343,598)
(344,599)(345,600)(346,576)(347,577)(348,578)(349,579)(350,580)(351,571)
(352,572)(353,573)(354,574)(355,575)(356,581)(357,582)(358,583)(359,584)
(360,585)(361,651)(362,652)(363,653)(364,654)(365,655)(366,646)(367,647)
(368,648)(369,649)(370,650)(371,656)(372,657)(373,658)(374,659)(375,660)
(376,636)(377,637)(378,638)(379,639)(380,640)(381,631)(382,632)(383,633)
(384,634)(385,635)(386,641)(387,642)(388,643)(389,644)(390,645)(391,621)
(392,622)(393,623)(394,624)(395,625)(396,616)(397,617)(398,618)(399,619)
(400,620)(401,626)(402,627)(403,628)(404,629)(405,630)(406,606)(407,607)
(408,608)(409,609)(410,610)(411,601)(412,602)(413,603)(414,604)(415,605)
(416,611)(417,612)(418,613)(419,614)(420,615)(421,696)(422,697)(423,698)
(424,699)(425,700)(426,691)(427,692)(428,693)(429,694)(430,695)(431,701)
(432,702)(433,703)(434,704)(435,705)(436,711)(437,712)(438,713)(439,714)
(440,715)(441,706)(442,707)(443,708)(444,709)(445,710)(446,716)(447,717)
(448,718)(449,719)(450,720)(451,666)(452,667)(453,668)(454,669)(455,670)
(456,661)(457,662)(458,663)(459,664)(460,665)(461,671)(462,672)(463,673)
(464,674)(465,675)(466,681)(467,682)(468,683)(469,684)(470,685)(471,676)
(472,677)(473,678)(474,679)(475,680)(476,686)(477,687)(478,688)(479,689)
(480,690);
poly := sub<Sym(960)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope